Casimir force in noncommutative Randall-Sundrum models

Nouicer, Khireddine; Youssef, Sabri

doi:10.1103/physrevd.80.086013

Cited by 5 publications

(17 citation statements)

References 51 publications

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“…Recently more attention of the physical community is also paid to the Casimir effect for parallel plates or piston in the braneworld, such as Randall-Sundrum models, etc. [38][39][40][41][42][43][44][45][46][47][48][49][50][51]. During the investigation above we can estimate the properties of the warped world which may be utilized to resolve the hierachy problem.…”

Section: Introductionmentioning

confidence: 99%

Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

Cheng

2012

Commun. Theor. Phys.

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We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified dimension. We obtain the Casimir energy density with the help of the regularization of multiple zeta function with one arbitrary exponent and further the renormalized Casimir energy density involving the thermal corrections. It is found that when the temperature is sufficiently high, the sign of the Casimir energy remains negative no matter how great the scale dimension δ is within its allowed region.We derive and calculate the Casimir force between the parallel plates affected by the fractal additional compactified dimension and surrounding temperature. The stronger thermal influence leads the force to be stronger. The nature of the Casimir force keeps attractive.

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Section: Introductionmentioning

confidence: 99%

Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

Cheng

2012

Commun. Theor. Phys.

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“…Majority of these works considered scalar field instead of electromagnetic field since scalar field is much more easier to deal with. In [16,18,21,27,28], electromagnetic field were considered but using the scalar field -electromagnetic field analogy that works in Minskowski spacetime. To yield the correct limit when the size of the extra dimension goes to zero, it was claimed that for the part corresponding to Casimir effect in 4D, the Casimir energy due to electromagnetic field is twice the Casimir energy due to scalar field; whereas for the part corresponding to Kaluza-Klein excitations, the Casimir energy due to electromagnetic field is three times the Casimir energy due to scalar field.…”

Section: Introductionmentioning

confidence: 99%

Casimir effect of electromagnetic field in Randall-Sundrum spacetime

Teo

2010

J. High Energ. Phys.

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We study the finite temperature Casimir effect on a pair of parallel perfectly conducting plates in Randall-Sundrum model without using scalar field analogy. Two different ways of interpreting perfectly conducting conditions are discussed. The conventional way that uses perfectly conducting condition induced from 5D leads to three discrete mode corrections. This is very different from the result obtained from imposing 4D perfectly conducting conditions on the 4D massless and massive vector fields obtained by decomposing the 5D electromagnetic field. The latter only contains two discrete mode corrections, but it has a continuum mode correction that depends on the thicknesses of the plates. It is shown that under both boundary conditions, the corrections to the Casimir force make the Casimir force more attractive. The correction under 4D perfectly conducting condition is always smaller than the correction under the 5D induced perfectly conducting condition. These statements are true at any temperature.Comment: 20 pages, 4 figure

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“…In a recent publication [1], K. Nouicer and Y. Sabri computed the Casimir force acting on a pair of parallel plates in the five dimensional Randall-Sundrum braneworlds of type I and type II. They computed the Casimir force to the first order in the noncommutative parameter and claimed that in Randall-Sundrum model of type I (RSI), the presence of noncommutativity will lead to repulsive Casimir force when the plate separation is small.…”

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confidence: 99%

“…If one considers massless scalar field with Dirichlet boundary conditions, one should take p = p ′ = 1. In [1], it was claimed that for electromagnetic field with perfectly conducting boundary conditions, one should set p ′ = 2 and p = 3 due to the polarizations of photons in * Electronic address: LeePeng.Teo@nottingham.edu.my 4D and 5D spacetime. For Casimir effect in extra dimensional spacetime as in the present scenario, it is actually questionable whether one can obtain the result for electromagnetic field by simply adding the polarization factors p ′ and p. Such an imposition of polarization factors for Casimir effect in spacetime with extra dimensions was first applied in the paper [4], and was later followed by other works such as [2,5,6].…”

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confidence: 99%

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Casimir force in noncommutative Randall-Sundrum models revisited

Teo

2010

Phys. Rev. D

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We propose another method to compute the Casimir force in noncommutative Randall-Sundrum braneworld model considered by K. Nouicer and Y. Sabri recently. Our method can be used to compute the Casimir force to any order in the noncommutative parameter. Contrary to the claim made by K. Nouicer and Y. Sabri that repulsive Casimir force can appear in the first order approximation, we show that the Casimir force is always attractive at any order of approximation.PACS numbers: 11.25. Mj, 11.10.Kk, 11.10.Nx In a recent publication [1], K. Nouicer and Y. Sabri computed the Casimir force acting on a pair of parallel plates in the five dimensional Randall-Sundrum braneworlds of type I and type II. They computed the Casimir force to the first order in the noncommutative parameter and claimed that in Randall-Sundrum model of type I (RSI), the presence of noncommutativity will lead to repulsive Casimir force when the plate separation is small.In this report, we present another computation method that allows us to compute to any order of the noncommutative parameter, and investigate whether noncommutativity will change the nature of the Casimir force. Let κ be the parameter governing the degree of curvature of the RSI model. Define ξ = πκe −πκR and let l be the fundamental noncommutative length scale. The Casimir energy between a pair of parallel plates with distance a apart is given bywhere A is the area of the plates and v = 2 accounts for the volume of the orbifold [3]. The eigenfrequencies ω nN are given bywhere κ N , N = 0, 1, 2, . . . , are the effective masses due to the existence of the extra dimension, and κ 0 = 0. We put the factors p ′ and p in (1) so that we can compare to [1]. If one considers massless scalar field with Dirichlet boundary conditions, one should take p = p ′ = 1. In [1], it was claimed that for electromagnetic field with perfectly conducting boundary conditions, one should set p ′ = 2 and p = 3 due to the polarizations of photons in * Electronic address: LeePeng.Teo@nottingham.edu.my 4D and 5D spacetime. For Casimir effect in extra dimensional spacetime as in the present scenario, it is actually questionable whether one can obtain the result for electromagnetic field by simply adding the polarization factors p ′ and p. Such an imposition of polarization factors for Casimir effect in spacetime with extra dimensions was first applied in the paper [4], and was later followed by other works such as [2,5,6]. However, the Casimir effect of electromagnetic field in spacetime with extra dimensions is actually not that simple, and it highly depends on the geometry of the extra dimensions and on how one interprets the perfectly conducting boundary conditions. Different approaches will lead to different results, and one may not be able to obtain the correct 4D limit when the size of the extra dimensions vanishes. Therefore majority of the works in Casimir effect in spacetime with extra dimensions work with scalar field rather than electromagnetic field. Nevertheless, it should be pointed out that in the r...

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Casimir force in noncommutative Randall-Sundrum models

Cited by 5 publications

References 51 publications

Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

Casimir effect of electromagnetic field in Randall-Sundrum spacetime

Casimir force in noncommutative Randall-Sundrum models revisited

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